Please solve for all three parts of the question.

Mathematics

1 answer:

neonofarm [45]3 years ago

5 0

Answer:

f(-5) = 25

f(0) = -2

f(5) = 16

Step-by-step explanation:

Given the functions;

To get f(-5), we will use the function of x where x is less than 0 since -5 is less than zero

at where x < 0, f(x) = x^2

f(-5) = (-5)^2

f(-5) = 25

b) For f(0), where the point where x = 0, f(x)= -2

Hence the value of f(o) = -2

c) For f(5), the function where x > 5 is f(x) = 2x+6

f(x) = 2x+6

f(5) = 2(5)+6

f(5) = 16

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sweet [91]

Answer:

a) y = 10x +500

b) $500

c) $15 for 100; $10.50 for 1000

Step-by-step explanation:

We assume the given "cost per unit" is the variable cost per unit. The total cost (y) for x units, given some fixed cost (b), is ...

y = 10x +b

For 100 units, this is ...

1500 = 10(100) +b

500 = b . . . . . . . . subtract 1000

The cost function rule is ...

y = 10x +500

The fixed cost is the cost of producing 0 units:

y = 10(0) +500

y = 500 . . . . . . . the fixed cost in dollars

The average cost (ac) of producing n units is the total cost divided by n:

ac(n) = (10n +500)/n = 10 +500/n

The average cost for 100 units is

ac(100) = 10 +500/100 = 15 . . . average dollar cost for 100 units

The average cost for 1000 units is ...

ac(1000) = 10 +500/1000 = 10.50 . . . average dollar cost for 1000 units

4 0

3 years ago

Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = −1

VikaD [51]

Answer:

Step-by-step explanation:

If you plot the focus and the directrix you see that the focus is above the directrix. Since a parabola always wraps itself around the focus, this parabola opens upwards and has the standard form equation:

$(x-h)^2=4p(y-k)$ where h and k are the coordinates of the vertex and p is the number of units between the vertex and the focus, or the vertex and the directrix. This number of units will be the same for both since the vertex is smack dab inbetween the focus and the directrix. The focus is also on the axis of symmetry, which means that it shares the x coordinate with the vertex (which is actually the h coordinate) of -5. Halfway between the y value of 5 and the y value of -1 is 2. So the vertex is located at (-5, 2). The number of units between the vertex and the focus is 3, so the equation is: